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/gone

 Dec 9, 2019
edited by whoisjoe  Jan 7, 2020
 #1
avatar+106539 
+1

Area of right triangle  =  (1/2)(BC ) (BA)       (1)

 

Two white areas  that  are between the   gray areas  and triangle ABC  =  area of semi-circles  - area of  ABC  =

 

(1/2)  [ pi (AC/2)^2 -  (BC)(BA)  ]  =   (1/2) [ pi ( BC^2 + BA^2)/4  - (BC)(BA)   ]   (2)      

 

Area   of   grey semi-circles  =  (1/2)pi [  (BC/2)^2  + ( BA/2)^2  ]   -  (2)   =

 

(1/2) pi  [ (BC^2 + BA^2)/4 ]   -  (1/2)  [ pi (BC^2  + BA^2)/4 - (BC)(BA) ]   =

 

-(1/2) [ - (BC)(BA)  ]   =

 

(1/2)(BC)(BA)   which  =  (1)

 

So....true  !!!

 

 

cool cool cool

 Dec 9, 2019

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